E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands

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RELIABILITY OF EXISTING HYDRAULIC STRUCTURES

CLAUS KUNZ(1)

(1) Bundesanstalt fuer Wasserbau, Kussmaulstrasse 17, D-76187 Karlsruhe (Germany)

claus.kunz@baw.de

ABSTRACT

Hydraulic structures are long-living infrastructure assets which have to some extent a high risk potential. Waterway structures in Germany have an average lifespan of 65 years already, about 25% of the structures have already passed their theoretical service life of 100 years. By aging and degradation, by changing of environmental conditions with time, but also by changes of safety concepts and proof formats in codes existing structures must be evaluated within a statical verification or a risk analysis. This is not possible with the standards that have often been usually designed only for new structures. The application of these “new structure” standards leads to a conceptional aging, where the bearing capacity is not given by computational figures. However this does not correspond to reality. In addition, limited resources prohibit to meet the safety standard ever for new structures during a cycle of use, and thus to negate the aging.

A concept for the reliability of massive hydraulic structures had been developed, where

- the remaining lifetime, - the possible modification of basic variables on the action and resistance side after some detailed on-site inventory and - risk considerations

are comprised.

Keywords: safety, reliability, existing hydraulic structures, Eurocode, water action

1. INTRODUCTION

Hydraulic structures are long-living infrastructure assets which have to some extent a high risk potential. Waterway structures in Germany have an average lifespan of 65 years already, about 25% of the structures have already passed their theoretical service life of 100 years. By aging and degradation, by changing of environmental conditions with time, but also by changes of safety concepts and proof formats in codes existing structures must be evaluated within a static verification or a risk analysis. This is not possible with the standards that have often been usually designed only for new structures. The application of these “new structure” standards leads to a conceptional aging, where the bearing capacity is not given by computational figures. However this does not correspond to reality. In addition, limited resources prohibit to meet the safety standard ever for new structures during a cycle of use, and thus to negate the aging.

2. SAFETY CONCEPT FOR (HYDRAULIC) STRUCTURES

The currently valid design standards in Germany and many other countries apply to new buildings. European codes are based on the Eurocode which is an overall construction type concept according EN 1990 (2002).

Figure 1: Concept of Lifetime Orientated Design

E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands

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Background of the safety concept is a design lifetime orientated safety concept where the safety of structures or structural

elements has to be ensured by a target reliability over the design lifetime TN , see BauPVO (2013). The safety is described by the uncertainties of the used models (e.g. model for the action determination, for the static system, for the resistance, etc.) and of the scattering basis variables for actions and resistances as time-invariant influences, figure 1.

The standards based on the Eurocode concept are based on a semi-probabilistic safety concept in which the uncertainties of actions (e.g. loads as water pressure, earth pressure, self-weight, etc.) and resistances (e.g. material strengths) are considered each by characteristic values Fk,i and corresponding partial safety factors ɣF,i .

M

k

ikiF

i

i

RF

,,

1

(1)

where:

i = number of simultaneously considered actions

γF = partial safety factor for the action,

Fk = characteristic value of the action,

γM = partial safety factor for the resistance,

Rk = characteristic value of the resistance.

Using the resulting design values, the formula above can also be written by Ed ≤ Rd . Within different design situations the structure’s lifetime is verified within normal using condition (persistant design situations, P), erection, repair and inspection conditions (transient design situations, T) and short and extreme conditions (accidental design situations, A). Actions are differentiated by permanent action (e.g. self-weight, earth pressure), temporary actions (e.g. water pressure, wind, snow) and accidental actions (e.g. impact). The desired level of safety which must be fulfilled depends on the type of structure. Hydraulic structures are assigned to an overall required operational failure probability Pf = 10

-4 per lifetime TN = 100 years,

see DIN 19702 (2013) and KUNZ (2013). This corresponds to a reliability index βTN=100 = 3.8. The yearly operational failure probability is back calculated to pf = 8*10

-7 /a. The yearly failure probability for hydraulic structures is lower than that

for normal buildings.

Within a semi-probabilistic design concept these reliability requirements shall be fulfilled by determination of characteristic values Fk, by using the above mentioned partial safety factors ɣF,i within design situations and by differentiation between a unfavorable or favorable effect of the considered action, ɣF,i,sup or ɣF,i,inf . Characteristic values are determined as a quantile of their probability function; permanent actions are often represented by their mean value, temporary actions by their exceedance probability Ft = 1/TN , resistance values are represented by their 5%-quantile.

Table 1 shows the partial safety factors for actions for the structural design (STR) and for the bearing capacity (Ultimate Limit State, ULS) of new concrete hydraulic structures, acc. DIN 19702 (2013).

Table 1: Partial safety factors for new solid hydraulic structures in Germany, acc. DIN 19702 (2013)

Limit State Action ULS Design Situation

P T A

STR

permanent

unfavourable G,sup 1.35 1.20 1.00

favourable G,inf 1.00 1.00 1.00

temporary

unfavourable Q,sup 1.50 1.30 1.00

water pressure,

favourable Q,inf 0.80 0.90 1.00

others favourable Q,inf 0 0 0

accidental - A

-

-

1.00

Such a semi-probabilistic design concept is used for hydraulic (and other) structures in different countries of the world, see PIANC (2015).

E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands

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Existing hydraulic structures do no longer meet the current new-structures standards in many cases, characterized by updates and knowledge increases and by new reliability concepts. Unlike with new construction, where uncertainties in planning, in erection, for actions and resistances and for durability have to take into account, in existing structures findings from eligible inventories (e.g. geometry, knowledge of the structural system, measurements of pressures, testing of material properties, etc.) might be used to reduce the uncertainties contained in the standard concept. Additionally socially adequate reliability goals might be implemented.

3. REMAINING EXPECTANCY CONCEPT

The safety concept for existing hydraulic structures takes full advantage of the useful life-oriented safety concept of the Eurocodes in consideration target reliability or target failure probability and service life. Furthermore, experiences out of the operation of the structure will be used for the recalculating verification of the bearing capacity on a probabilistic basis where variables and their uncertainties are taken into account. During operation uncertainties from the time of erection are no longer existent. Therefore, for existing buildings target reliability level over the remaining lifetime, the partial safety factors as well as the determination of the characteristic values might be adjusted.

The principle of lifetime design includes a total failure probability FT (t) for the verification of a structural member as a function of its lifetime, which is calculated from the annual "operational" failure probability pf and the adjacent design lifetime TN, see SCHÜELLER (1981).

FT (t) = 1 – (1 – pf)TN

(2)

Considering the total design lifetime of a structure a not occurred exceedance of the scheduled scattering of basic variables or a not happened failure in the past might be used as knowledge about the structure and might be taken into account for charging the reliability of the forthcoming remaining lifetime (remaining expectancy).

Starting with the total overall failure probability FTN (t) which is expressed by:

FTN (t) = 1 – (1 – pf)TN

= Φ (- βTN) (3)

The yearly failure probability is given by:

( ( ) )

(4)

with

β= reliability index

TN = design lifetime

TRN= remaining lifetime (expectancy)

pf,1= yearly failure probability

Φ= inverse GAUSSIAN distribution

FTN (t) = total overall failure probability for the design lifetime TN ( equivalent to Pf,TN )

The expectancy concept allows a transfer of the total overall probability of failure to the remaining lifetime TRN = TN - t of an existing structure, if at time t no failure has occurred. When compared to the case of a new structure with the required same overall failure probability, the annual probability of failure thereby increases to

( ( ) )

(5)

E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands

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For the determination of partial safety factors in the context of the partial safety concept according to EN 1990 (2002), in

which as principle basic variables for a 100-year lifetime are used, an equivalent reliability index βTRN is calculated by

referring the annual failure probability for the remaining lifetime, , on a 100 years period.

( ) ( ( ( ) )

(6)

The attachable required "operational" reliability index βTRN for the verification of a hydraulic structure with a remaining lifetime TRN <100 a is shown in figure 2, red curve. The basic verification principle is that the reliability covering the remaining lifetime TRN is adjusted in that way so that the original overall target reliability FT (t) is observed as for a new structure, so that the social-adequate safety is maintained. Modification of the reliability index β leads to a lower partial safety factor so that existing structures might be regarded as safe enough. If, for example, a hydraulic structure is assessed for a remaining lifetime of 20 years, the consistent application of this expectancy concept allows an equivalent

target reliability index of TRN, 20 = 3.4 instead of 3.8, see figure 2. In case no change in operation or no rehabilitation is foreseen, a suitable period for the verification of a hydraulic structure might be TRN = 30 years which is a time where someone could react when the safety is not sufficient and may plan strengthening. This remaining lifetime has been

proposed for the verification of hydraulic structures, BAW (2015). The adjacent TRN, 30 = 3.5.

Figure 2: Equivalent reliability index for hydraulic structures, new structures (blue line), existing structures during

remaining expectancy (red line), normal buildings (green line), from KUNZ;STAUDER (2013)

4. WATER ACTION

Water pressure is one of the dominant action to hydraulic structures and will here be described by its statistics. According the Eurocode principles for water as a variable action the partial safety factor might be assumed by ɣF,sup = 1.5, in case of a geometrical limit by ɣF,sup = 1.35, see table 1. For the updating of DIN 19702 (2013) some investigations had been performed to prove the partial safety factor for water pressure ɣF,sup as unfavorable effect, see KUNZ (2014). The uncertainty of the water pressure results from the uncertainty of the adjacent water level. Instead of lacking measurements in the vicinity of hydraulic structures typical longtime level measurements in German (navigable) rivers as well as some groundwater measurements had been analysed by using the suitable GUMBEL distribution function. Thereby was assumed that the water level variation in a river systems reflects the water level variation besides hydraulic structures in such a river system.

GUMBEL leads to the water level as a quantile p:

2,40

2,60

2,80

3,00

3,20

3,40

3,60

3,80

4,00

4,20

4,40

4,60

4,80

5,00

0 10 20 30 40 50 60 70 80 90 100

Bezugszeitraum [Jahre]

Zuve

rläs

sigk

eit

sin

de

x b

Zuverlässigkeitsniveau Wasserbau

(Neubau), b100 = 3,8

Zuverlässigkeitsniveau Eurocode

(Neubau), b50 = 3,8

Zuverlässigkeitsniveau Wasserbau (Bestand)

in Abhängigkeit der Restnutzungsdauer

E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands

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hp = hm * (1 – 0.7797 * VW (0.57722 + ( ln ( -ln p)))) (7)

with:

hp: quantile of the sample,

hm: mean value of the sample,

VW: coefficient of variation of the sample (VW = σh / hm ).

Using the characteristic value hk as the 99%-quantile for hydraulic structures, because design lifetime should be 100 years according DIN 19702 (2013), it follows:

h99 = hk = hm * (1 + 3.136678 * VW) (8)

The design value for the water level is calculated by:

hd = hm - h (0.4501 + 0.7797 (ln (-ln (E • erf. )))) (9)

with:

h: standard deviation of the sample,

E: sensitivity factor of the action, here acc. EN 1990 (2002) E = - 0.7,

erf. : the required reliability index, here acc. DIN 19702 erf. = 3.8,

and conversed to:

hd = hm + 3.8950 * h = hm * (1+ 3.8950 * VW) (10)

whereas the partial safety factor for the water level is:

f,h = hd / hk = (hm * (1+ 3.8950 * VW))/ (hm * (1 + 3.136678 * VW)) (11)

or

f,h = (1+ 3.8950 * VW)/ (1 + 3.136678 * VW)(12)

and is shown in figure 3, see KUNZ (2014). Note that this partial safety factor is only the safety factor for the single water level, not yet for the action or the effect of this water level.

Figure 3: Partial safety factor f,h for the single water level over the coefficient of variation Vw

1

1,02

1,04

1,06

1,08

1,1

1,12

1,14

1,16

1,18

1,2

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

coefficient of variation Vw

yf,

h

E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands

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The analysis of typical water level measurements in German rivers, data collection had been 40 years, and the evaluation of a confidence interval with 95% lead to coefficients of variation (COV) with a spread of Vw between 0.12 and 0.53.

Partial safety factors f,h show a spread between 1.07 and 1.15 with a mean f,h = 1.12, corresponding to a coefficient of variation of Vw = 0.35. The most conservative assumption of the effect of such a water level acting on a structural element is a “cantilever model” where the single water level acts in his 3

rd power. Therefore a suitable partial safety factor for the

effect of variable water pressure has been found with:

F,sup = f,h 3 * Sd = 1.12

3 * 1.10 = 1.40 * 1.10 = 1.545 1.50 (13)

where Sd represents the model safety factor which is taken as Sd = 1.1. This value corresponds well to the F,sup = 1.5 in

table 1 and may be used for calibration.

For existing hydraulic structures and a remaining lifetime of TRN = 30 a, TRN, 30 = 3.5, the partial safety factor can be

modified to F,sup,30a = 1.25 which is smaller than 1.5. When statistical information is available the partial safety factor for an existing hydraulic structure may be modified as shown in figure 4, now shown for the partial safety factor for the action effect according equation (13).

Figure 4: Partial safety factor ɣQ for the water pressure and for existing structures with TRN = 30 a (β = 3.5), dependent on

variation Vw

5. FUTURE RESEARCH

The verification of existing hydraulic structures and their reliability requirement would need some more research concerning the other relevant and dominating action like earth pressure, BAW (2014). Another aspect with the safety concept according EN 1990 (2002) and adjacent codes is the big dimension of hydraulic structures where someone had to think about it whether a local exceedance of an action meets a local shortfall of a resistance which may lead to a failure according the safety theory. At least the social adequate overall target reliability for existing structures which might not be the same as for new structures can be analysed and modified.

6. CONCLUSION

Starting with the problem of the evaluation of existing hydraulic structures considering a need of static verification a method has been developed to determine the reliability as time-dependent safety for the remaining lifetime. This method, called remaining expectancy concept, is based on the design concept of the Eurocodes which is a reliability-based design procedure. The method considers the principles of the common maintenance strategies and allows the safe and economic verification of existing structures considering their experienced lifetime. The method uses the methodology of modern partial safety concept by modifying the overall target reliability on one hand side and statistical information about the variability of basic variables.

1,05

1,1

1,15

1,2

1,25

1,3

1,35

1,4

0 0,1 0,2 0,3 0,4 0,5 0,6

coefficient of variation Vw

partial safety factor ɣ

E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands

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A concept for the reliability of solid hydraulic structures had been developed, where

- the remaining lifetime, - the possible modification of basic variables on the action and resistance side after some detailed on-site inventory and - risk considerations

are comprised. For example, the required total reliability according Eurocode for a new structure which implies several uncertainties is recognized for the remaining lifetime as the structure experienced had shown no failure up to the valuation

date. The equivalent reliability index can be adapted for the remaining service time. Measurements and stochastical treatments of relevant actions, such as (flood) water levels and groundwater levels, but also soil properties and material testing of concrete and steel properties allows updated base variables (means, standard deviations). For proof in a semi-probabilistic way modified partial safety factors for actions and resistances are gained. An appropriate safety evaluation of existing hydraulic structures is aimed.

REFERENCES

BauPVO (2013): Bauprodukte-Verordnung: Verordnung (EU) Nr. 305/2011 des europäischen Parlaments und des Rates vom 9. März 2011 zur Festlegung harmonisierter Bedingungen für die Vermarktung von Bauprodukten und zur Aufhebung der Richtlinie 89/106/EWG des Rates. EU-Amtsblatt L 88, 04.04.

BAW (2014): FuE-Bericht: „Sicherheitstheoretische Studien für bestehende Wasserbauwerke“, BAW-Nr. A39510070001-01, Dezember 2014.

DIN 19702 (2013): Massivbauwerke im Wasserbau – Tragfähigkeit, Gebrauchstauglichkeit und Dauerhaftigkeit. Beuth-Verlag, Berlin, 2013.

EN 1990 (2002): Basis of design – General rules. CEN, Brussels. KUNZ, C. (2013): Wasserbauwerke aus Beton nach europäischen Normen. In: Betonbauteile nach Eurocode 2. Hrsg.:

Holschemacher, K., HTWK Leipzig, Beuth Verlag, Berlin, 2013. KUNZ, C. (2014): Ein Beitrag zum Teilsicherheitsbeiwert für Wasserdruck. In: Bautechnik 91 (2014), Heft 5. Verlag Ernst

& Sohn, Berlin 2014. KUNZ, C.;STAUDER, F. (2013): Sicherheitskonzept für bestehende Wasserbauwerke. In: Bautechnik-Tag 2013,

Tagungsband, Hamburg, 11. bis 12.04.2013. Deutscher Beton- und Bautechnik-Verein. PIANC (2015): PIANC report n° 140-2015. Semi-probabilistic design concept for inland hydraulic structures. PIANC,

Brussels, 2015 (in preparation). SCHÜELLER, G. (1981): Einführung in die Sicherheit und Zuverlässigkeit von Tragwerken. Verlag von Wilhelm Ernst &

Sohn, Berlin München, 1981.